Order Statistics in the Farey Sequences in Sublinear Time

We present the rst sublinear-time algorithms for computing order statistics in the Farey sequence and for the related problem of ranking. Our algorithms achieve a running times of nearly O(n2/3 ), which is a signicant improvement over the previous algorithms taking time O(n). We also initiate the study of a more general problem: counting primitive lattice points inside planar shapes. For rational polygons containing the origin, we obtain a running time proportional to D6/7 , where D is the diameter of the polygon.

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Jakub Pawlewicz
• Keywords: Algorithms Taking Time, ESA 2007, Farey Sequence, Rst Sublinear-time Algorithms